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Abstract
For an integral domain
D , the
irreducible divisor graph G D ( x )
of a nonunit
x
∈
D
gives a visual representation of the factorizations of
x . Here we
consider a higher-dimensional generalization of this notion, the
irreducible divisor simplicial
complex S D ( x ) .
We show how this new structure is a true generalization
of G D ( x ) ,
and show that it often carries more information about the
element x and
the domain
D
than its two-dimensional counterpart.
Keywords
factorization, simplicial complex
Mathematical Subject Classification 2010
Primary: 13A05
Secondary: 55U10
Milestones
Received: 6 August 2012
Revised: 12 October 2012
Accepted: 15 October 2012
Published: 8 October 2013
Communicated by Scott Chapman